Problem: There are some tasks which have the following structure: you are given a model, and you can do some operations, you should use these operations to achive the goal. One way to create a new task is to use the same model and same operations, but change the goal.

Let's have a try. I have created the following task for Topcoder SRM 557 Div1-Hard: you are given n integers x1, x2, ..., xn. You are allowed to perform the assignments (as many as you want) of the following form xi ^= xj (in the original task i and j must be different, but in this task we allow i to equal j). The goal is to maximize the sum of all xi.

Now we just change the goal. You are also given n integers y1, y2, ..., yn. You should make x1, x2, ..., xn exactly equal to y1, y2, ..., yn. In other words, for each i number xi should be equal to yi.

Input

The first line contains an integer n (1 ≤ n ≤ 10000). The second line contains n integers: x1 to xn (0 ≤ xi ≤ 109). The third line contains n integers: y1 to yn (0 ≤ yi ≤ 109).

Output

If there is no solution, output -1.

If there is a solution, then in the first line output an integer m (0 ≤ m ≤ 1000000) – the number of assignments you need to perform. Then print m lines, each line should contain two integers i and j (1 ≤ i, j ≤ n), which denote assignment xi ^= xj.

If there are multiple solutions you can print any of them. We can prove that under these constraints if there exists a solution then there always exists a solution with no more than 106 operations.

Examples

Input

2
3 5
6 0


Output

2
1 2
2 2


Input

5
0 0 0 0 0
1 2 3 4 5


Output

-1


Input

3
4 5 6
1 2 3


Output

5
3 1
1 2
2 2
2 3
3 1


Input

3
1 2 3
4 5 6


Output

-1

Note

Assignment a ^= b denotes assignment a = a ^ b, where operation "^" is bitwise XOR of two integers.

Solution (in JAVA):

Solution:
import java.util.List;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.ArrayList;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.Collection;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskF solver = new TaskF();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskF {
    private static final int BIT = 30;

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int[] source = new int[n];
        int[] target = new int[n];
        for (int i = 0; i < n; ++i)
            source[i] = in.nextInt();
        for (int i = 0; i < n; ++i)
            target[i] = in.nextInt();
        int[] importantBitOfSource = new int[BIT];
        int[] importantBitOfTarget = new int[BIT];
        List<int[]> moveFromSource = new ArrayList<>();
        List<int[]> moveFromTarget = new ArrayList<>();
        gauss(source, importantBitOfSource, moveFromSource);
        gauss(target, importantBitOfTarget, moveFromTarget);
        List<int[]> moves = new ArrayList<>();
        moves.addAll(moveFromSource);
        for (int i = 0; i < n; ++i) {
            int last = i;
            for (int bit = 0; bit < BIT; ++bit)
                if ((source[i] & 1 << bit) != (target[i] & 1 << bit)) {
                    while (last < n && Integer.numberOfTrailingZeros(source[last]) < bit)
                        ++last;
                    if (last < n && Integer.numberOfTrailingZeros(source[last]) == bit) {
                        source[i] ^= source[last];
                        moves.add(new int[]{i, last});
                    } else {
                        out.println(-1);
                        return;
                    }
                    ++last;
                }
        }
        Collections.reverse(moveFromTarget);
        moves.addAll(moveFromTarget);
        out.println(moves.size());
        for (int[] move : moves) {
            out.print(move[0] + 1);
            out.print(' ');
            out.println(move[1] + 1);
        }
    }

    private void gauss(int[] a, int[] importantBit, List<int[]> move) {
        int n = a.length;
        Arrays.fill(importantBit, -1);
        for (int bit = 0, last = 0; bit < BIT; ++bit) {
            boolean found = false;
            for (int x = last; x < n; ++x)
                if ((a[x] & 1 << bit) != 0) {
                    if (x != last) {
                        a[x] ^= a[last];
                        a[last] ^= a[x];
                        a[x] ^= a[last];
                        move.add(new int[]{x, last});
                        move.add(new int[]{last, x});
                        move.add(new int[]{x, last});
                    }
                    found = true;
                    break;
                }
            if (!found) continue;
            importantBit[bit] = last;
            for (int x = last + 1; x < n; ++x)
                if ((a[x] & 1 << bit) != 0) {
                    a[x] ^= a[last];
                    move.add(new int[]{x, last});
                }
            ++last;
        }
    }
}

class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

}